De novo copy-number variants (CNVs) can cause neuropsychiatric disease, but the degree to which they occur somatically, and during development, is unknown. Single-cell whole-genome sequencing (WGS) in >200 single cells, including >160 neurons from three normal and two pathological human brains, sensitively identified germline trisomy of chromosome 18 but found most (≥95%) neurons in normal brain tissue to be euploid. Analysis of a patient with hemimegalencephaly (HMG) due to a somatic CNV of chromosome 1q found unexpected tetrasomy 1q in ∼20% of neurons, suggesting that CNVs in a minority of cells can cause widespread brain dysfunction. Single-cell analysis identified large (>1 Mb) clonal CNVs in lymphoblasts and in single neurons from normal human brain tissue, suggesting that some CNVs occur during neurogenesis. Many neurons contained one or more large candidate private CNVs, including one at chromosome 15q13.2-13.3, a site of duplication in neuropsychiatric conditions. Large private and clonal somatic CNVs occur in normal and diseased human brains.